[Physics] Energy of electrons in wire

electronsflow

The Drude Model helped me quite a lot to visualize how current could flow in a circuit. However, there is still a point that I cannot grasp in the explanation given by some people when they talk about energy. When considering a round trip of one electron along a circuit, it is usually said that :

The electron gains energy when going through the battery and loses that energy along the wire as it collides with the lattice of the conductor.

My problem with this reasoning is that it is implying that the electron has more energy when it leaves the battery than anywhere else in the circuit. However, according to the Drude model, when the electrons collide with the lattice, they indeed lose kinetic energy but they regain kinetic energy as soon as they start accelerating thanks to electric fields produced along the wire. This causes electrons to have an average drift speed. In other words, their kinetic energy is constant on average, which is at first glance, in contradiction with the reasoning given above. What am I missing here?

Best Answer

The electron gains potential energy in the battery; this is transformed to kinetic energy, which from time to time gets dissipated in the inelastic collisions with the lattice.

It's quite analogous to a (semi-elastic) ball jumping down some stairs (and then, in the battery, taking the elevator to get up again). This might be more intuitive.